A delivery device of this type is known for example from DE 10 2011 084 542 A1. In the case of the delivery device, the oil pump is driven selectively by the direct drive or by the activatable electric drive parallel operation of both drives is also possible. The delivery power of the oil pump is increased if the direct drive is running in operating state with too low a rotational speed. The state arises in rare situations in the case of high demands being placed on the internal combustion engine. This however has the effect that the oil pump must be configured for an adequate delivery power of the direct drive for the base load. In practice, this means that the oil pump must be of very large dimensions. Such large dimensioning is however very disruptive in the case of internal combustion engines.